Development of a digital twin of a powertrain for efficiency estimations with machine learning and physical modeling

Development of a digital twin of a powertrain for efficiency estimations with machine learning and physical modeling | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Development of a digital twin of a powertrain for efficiency estimations with machine learning and physical modeling Lennart Kopp, Niels Ockert, Luca Cadau, Markus Kley This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7990839/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Accurate prediction of the efficiency of electromechanical powertrains is crucial for the development of electric vehicles. Until now, this has been done through time-consuming and costly test bench investigations in late development phases. To address that, digital modeling and development processes are implemented in the product development process. Although, existing modeling approaches such as simulations or classical data-driven models often have limitations in terms of prediction accuracy, prediction speed, or model size. To address this problem, this paper develops five different data-driven modeling approaches for digital twins, ranging from simple black-box models to hybrid grey-box approaches. In addition, a sixth modeling approach, a white-box model, was conducted as a reference to the other model approaches. Validation is based on recorded measurement data from a test bench setup of an electromechanical powertrain consisting of a permanent magnet synchronous machine and a multi-stage transmission. The evaluation includes classic error metrics such as mean absolute error and mean relative error, but also model size, training times, and prediction speeds. In addition, a quotient of input and output variables is included, which is used to evaluate the information content of the model structure. Despite a slightly increased error tolerance, the final bright-grey-model approach offers the best compromise between prediction accuracy, real-time capability, and a high output-to-input quotient. The results demonstrate that data-driven digital twins with physically informed structures enable early and real-time prediction of the efficiency of electromechanical powertrains. Digital Twin Powertrain Machine Learning AI Test rig Frontloading Product development Efficiency estimation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 05 May, 2026 Reviews received at journal 11 Apr, 2026 Reviewers agreed at journal 04 Apr, 2026 Reviewers invited by journal 10 Nov, 2025 Editor assigned by journal 04 Nov, 2025 Submission checks completed at journal 04 Nov, 2025 First submitted to journal 30 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7990839","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":542607666,"identity":"69a06ae8-e919-458f-87bf-9e2070bcce88","order_by":0,"name":"Lennart 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modeling","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"advanced-modeling-and-simulation-in-engineering-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"amos","sideBox":"Learn more about [Advanced Modeling and Simulation in Engineering Sciences](http://amses-journal.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/amos/default.aspx","title":"Advanced Modeling and Simulation in Engineering Sciences","twitterHandle":"@SpringerEng","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Digital Twin, Powertrain, Machine Learning, AI, Test rig, Frontloading, Product development, Efficiency estimation","lastPublishedDoi":"10.21203/rs.3.rs-7990839/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7990839/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAccurate prediction of the efficiency of electromechanical powertrains is crucial for the development of electric vehicles. Until now, this has been done through time-consuming and costly test bench investigations in late development phases. To address that, digital modeling and development processes are implemented in the product development process. Although, existing modeling approaches such as simulations or classical data-driven models often have limitations in terms of prediction accuracy, prediction speed, or model size. To address this problem, this paper develops five different data-driven modeling approaches for digital twins, ranging from simple black-box models to hybrid grey-box approaches. In addition, a sixth modeling approach, a white-box model, was conducted as a reference to the other model approaches. Validation is based on recorded measurement data from a test bench setup of an electromechanical powertrain consisting of a permanent magnet synchronous machine and a multi-stage transmission.\u003c/p\u003e\u003cp\u003eThe evaluation includes classic error metrics such as mean absolute error and mean relative error, but also model size, training times, and prediction speeds. In addition, a quotient of input and output variables is included, which is used to evaluate the information content of the model structure. Despite a slightly increased error tolerance, the final bright-grey-model approach offers the best compromise between prediction accuracy, real-time capability, and a high output-to-input quotient. The results demonstrate that data-driven digital twins with physically informed structures enable early and real-time prediction of the efficiency of electromechanical powertrains.\u003c/p\u003e","manuscriptTitle":"Development of a digital twin of a powertrain for efficiency estimations with machine learning and physical modeling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-19 12:50:34","doi":"10.21203/rs.3.rs-7990839/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-05-05T10:56:28+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-04-11T22:26:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"311603877014429076673869100191672134611","date":"2026-04-04T11:51:43+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-10T07:49:17+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-11-05T04:36:30+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-11-04T08:56:06+00:00","index":"","fulltext":""},{"type":"submitted","content":"Advanced Modeling and Simulation in Engineering Sciences","date":"2025-10-30T15:14:49+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"advanced-modeling-and-simulation-in-engineering-sciences","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"amos","sideBox":"Learn more about [Advanced Modeling and Simulation in Engineering Sciences](http://amses-journal.springeropen.com)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/amos/default.aspx","title":"Advanced Modeling and Simulation in Engineering Sciences","twitterHandle":"@SpringerEng","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e81879fb-b910-4aff-8ac5-093b3a41d5f1","owner":[],"postedDate":"November 19th, 2025","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-05T10:56:28+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-12T14:10:41+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-19 12:50:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7990839","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7990839","identity":"rs-7990839","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}